In this paper, we will study the existence and qualitative property of standing waves for the nonlinear Schrödinger equation , . Let and suppose that has k local minimum points. Then, for any , we prove the existence of the standing waves in having exactly l local maximum points which concentrate near l local minimum points of respectively as . The potentials and are allowed to be either compactly supported or unbounded at infinity. Therefore, we give a positive answer to a problem proposed by Ambrosetti and Malchiodi (2007) [2].
Keywords: Bound state, Multi-peak solutions, Nonlinear Schrödinger equation, Potentials compactly supported or unbounded at infinity
@article{AIHPC_2010__27_5_1205_0, author = {Ba, Na and Deng, Yinbin and Peng, Shuangjie}, title = {Multi-peak bound states for {Schr\"odinger} equations with compactly supported or unbounded potentials}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1205--1226}, publisher = {Elsevier}, volume = {27}, number = {5}, year = {2010}, doi = {10.1016/j.anihpc.2010.05.003}, zbl = {1200.35282}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2010.05.003/} }
TY - JOUR AU - Ba, Na AU - Deng, Yinbin AU - Peng, Shuangjie TI - Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 1205 EP - 1226 VL - 27 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2010.05.003/ DO - 10.1016/j.anihpc.2010.05.003 LA - en ID - AIHPC_2010__27_5_1205_0 ER -
%0 Journal Article %A Ba, Na %A Deng, Yinbin %A Peng, Shuangjie %T Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 1205-1226 %V 27 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2010.05.003/ %R 10.1016/j.anihpc.2010.05.003 %G en %F AIHPC_2010__27_5_1205_0
Ba, Na; Deng, Yinbin; Peng, Shuangjie. Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, pp. 1205-1226. doi : 10.1016/j.anihpc.2010.05.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2010.05.003/
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